Tree search procedures for the blocks relocation problem with batch moves

This research investigates a blocks relocation problem with batch moves (BRP-BM) mainly arising from the operations at slab yards in iron and steel plants. Several recent types of bridge cranes used in hot rolling slab yards can handle up to three slabs in one move, resulting in a typical scenario of the BRP-BM. A lower bound of the number of moves for the BRP-BM is presented. A greedy algorithm and three tree search algorithms, including one based on compound moves, are designed to solve the BRP-BM. The lower bound and the algorithms are validated and extensively evaluated based on both existing instances and randomly generated instances. The results indicate that the tree search algorithm based on compound moves outperforms the other algorithms especially for large-sized instances. Roughly speaking, the relative number of moves decreases from 1 to 0.80 and to 0.75 if the batch size increases from 1 to 2 and then to 3.